Analysis of future power grid loading considering uncertainties for application of risk based grid planning

可再生能源工厂的整合、常规发电厂的同时拆除、由于部门耦合而产生的新负荷以及能源市场的自由化导致了未来电力生产的巨大不确定性，从而也给电网的负荷带来了巨大的不确定性。由于电力线路和电缆的规划周期较长，必须在现有的不确定未来发展的情况下进行电网扩建投资。在该项目的范围内，克里斯蒂安·雷坦兹教授的能源系统、能源效率和能源经济研究所将与亚松森大学的能源系统研究小组(Gerardo Blanco教授)共同开发一个数学和技术总体模型，用于在不确定因素下规划输电网。这使得能够在考虑实际不确定性的情况下确定未来电网负荷，并从这些不确定性中推断出最优投资决策。因此，首先必须对不确定性进行随机分析和建模。对于不同的时间步长，采用情景技术表示发电本地化引起的不确定性(第一阶段的不确定性)。第二阶段的不确定性由多变量分布函数表示，这些不确定性是在确定发电的本地化之后产生的，例如通过天气不确定性。为此，使用了Copula，这是一个可以确定单个变量的边际概率分布之间关系的函数。然后，推导出一个总体模型，该模型为第一阶段的每个场景分配多变量分布函数，从而使每个网格节点的输入变量通过概率密度函数(PDF)及其相关性来建模。结果是确定线负荷PDF的概率潮流计算的输入值。为此目的，进一步发展了点估计方法的方法，使该方法能够用于实际网格。所提出的方法将通过蒙特卡罗模拟得到验证。为了规划能源电网，需要一种在不确定情况下基于期望线路负荷做出最优投资决策的方法。为此，首先评估网格分析的结果，然后对其进行集中。然后，推导出一个成本函数，作为实物期权分析应用的基础。与现有技术相比，该方法代表了一种全新的方法。在现有技术中，几乎不考虑不确定性，概率潮流计算方法仅适用于较小的测试电网。此外，概率潮流计算与实物期权分析的结合还没有发生，并提供了许多新的可能性。

The integration of renewable energy plants, the simultaneous dismantling of conventional power plants, the new loads because of sector coupling and the liberalization of energy markets lead to great uncertainties in the future generation of electrical energy and thus also in the load of energy grids. Due to long planning horizons for power lines and cables, investments for grid expansion must be made under existing uncertain future developments.Within the scope of the project, the institute of energy systems, energy efficiency and energy economics from Prof. Christian Rehtanz (ie³) and the research group energy systems (GISE) at the University of Asuncion from Prof. Gerardo Blanco will jointly develop a mathematical and technical overall model that can be used to plan the transmission grid under uncertainties. This enables the determination of future grid loads, taking into account real uncertainties, and the deduction of optimal investment decisions from these. Therefore, the uncertainties must be analyzed and modeled stochastically in a first step. The uncertainties resulting from the localization of the power generation (uncertainties of stage one) are represented using the scenario technique for different time steps. The uncertainties of the second stage, which result after the determination of the localization of the power generation, e.g. through weather uncertainties, are represented by multivariate distribution functions. For this purpose, the copula is used, a function which can determine the relationship between the marginal probability distribution of individual variables. Subsequently, an overall model is derived, which assigns multivariate distribution functions to each scenario of the first stage, so that the input variables for each grid node are modeled by probability density functions (PDF) and their correlations. The results are the input values for the probabilistic load flow calculations which determine the PDF of the line load. For this purpose, the approaches of the point-estimate method are developed further to enable the usage of the method for real grids. The developed method will be verified by Monte-Carlo-simulations. In order to plan the energy grid, a method is then required which makes optimal investment decisions under uncertainties based on the expected line loads. For this purpose, the results of the grid analysis are evaluated first and are concentrated afterwards. Subsequently, a cost function is deducted, which is used as the basis for the application of real option analysis. The approach of path integrals is used for this purpose.This procedure represents a completely new approach compared to the state of the art, where the uncertainties are hardly taken into account and the methods of probabilistic load flow calculations work only on small test grids. Also the coupling of the probabilistic load flow calculations with real option analysis has not taken place, yet, and offers a lot of new possibilities.